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# general visualisation
library('ggplot2') # visualisation
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library('scales') # visualisation
library('patchwork') # visualisation

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library('RColorBrewer') # visualisation
library('corrplot') # visualisation
corrplot 0.84 loaded
# general data manipulation
library('dplyr') # data manipulation

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library('readr') # input/output

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library('vroom') # input/output
library('skimr') # overview
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library('tibble') # data wrangling
library('tidyr') # data wrangling
library('purrr') # data wrangling

Attaching package: 㤼㸱purrr㤼㸲

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library('stringr') # string manipulation
library('forcats') # factor manipulation

# specific visualisation
library('alluvial') # visualisation
library('ggrepel') # visualisation
library('ggforce') # visualisation
library('ggridges') # visualisation
library('gganimate') # animations
No renderer backend detected. gganimate will default to writing frames to separate files
Consider installing:
- the `gifski` package for gif output
- the `av` package for video output
and restarting the R session
library('GGally') # visualisation
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library('ggthemes') # visualisation
library('wesanderson') # visualisation
library('kableExtra') # display

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# Date + forecast
library('lubridate') # date and time

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library('forecast') # time series analysis
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This is forecast 8.12 
  Need help getting started? Try the online textbook FPP:
  http://OTexts.org/fpp2/
#library('prophet') # time series analysis
library('timetk') # time series analysis

# Interactivity
library('crosstalk')
library('plotly')
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# parallel
library('foreach')

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library('doParallel')
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Loading required package: parallel
library(vroom)
library(stringr)
library(tidyverse)
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train <- vroom(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/sales_train_validation.csv'), delim = ",", col_types = cols())
prices <- vroom(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/sell_prices.csv'), delim = ",", col_types = cols())
calendar <- read_csv(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/calendar.csv'), col_types = cols())

sample_submit <- vroom(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/sample_submission.csv'), delim = ",", col_types = cols())

extract_ts <- function(df){
  
  min_date <- as.Date("2011-01-29")
  
  df %>%
    select(id, starts_with("d_")) %>%  
    pivot_longer(starts_with("d_"), names_to = "dates", values_to = "sales") %>%
    mutate(dates = as.integer(str_remove(dates, "d_"))) %>% 
    mutate(dates = min_date + dates - 1) %>% 
    mutate(id = str_remove(id, "_validation"))
}

set.seed(4321)
foo <- train %>% 
  sample_n(50)

ts_out <- extract_ts(foo)

cols <- ts_out %>% 
  distinct(id) %>% 
  mutate(cols = rep_len(brewer.pal(7, "Set2"), length.out = n_distinct(ts_out$id)))

ts_out <- ts_out %>% 
  left_join(cols, by = "id")

pal <- cols$cols %>%
   setNames(cols$id)
shared_ts <- highlight_key(ts_out)

palette(brewer.pal(9, "Set3"))

gg <- shared_ts %>% 
  ggplot(aes(dates, sales, col = id, group = id)) +
  geom_line() +
  scale_color_manual(values = pal) +
  labs(x = "Date", y = "Sales") +
  theme_tufte() +
  NULL

filter <- bscols(
  filter_select("ids", "Sales over time: Select a time series ID (remove with backspace key, navigate with arrow keys):", shared_ts, ~id, multiple = TRUE),
  ggplotly(gg, dynamicTicks = TRUE),
  widths = c(12, 12)
)
Sum of bscol width units is greater than 12
bscols(filter)
foo <- train %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  mutate(id = 1)

bar <- extract_ts(foo)

gg <- bar %>% 
  ggplot(aes(dates, sales)) +
  geom_line(col = "blue") +
  theme_tufte() +
  labs(x = "Date", y = "Sales", title = "All aggregate sales")

ggplotly(gg, dynamicTicks = TRUE)
foo <- train %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  mutate(id = 1)

bar <- extract_ts(foo)

gg <- bar %>% 
  ggplot(aes(dates, sales)) +
  geom_line(col = "blue") +
  theme_tufte() +
  labs(x = "Date", y = "Sales", title = "All aggregate sales")

ggplotly(gg, dynamicTicks = TRUE)
foo <- train %>%
  group_by(state_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = state_id)

bar <- extract_ts(foo) %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates))

gg <- bar %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  theme_tufte() +
  labs(x = "Date", y = "Sales", title = "Monthly Sales per State")

ggplotly(gg, dynamicTicks = TRUE)
foo <- train %>%
  group_by(cat_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = cat_id)

bar <- train %>%
  group_by(store_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = store_id)

p1 <- extract_ts(foo) %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates)) %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  theme_hc() +
  theme(legend.position = "none") +
  labs(title = "Sales per Category", x = "Date", y = "Sales")

p2 <- train %>% 
  count(cat_id) %>% 
  ggplot(aes(cat_id, n, fill = cat_id)) +
  geom_col() +
  theme_hc() +
  theme(legend.position = "none") +
  theme(axis.text.x = element_text(size = 7)) +
  labs(x = "", y = "", title = "Rows per Category")

p3 <- extract_ts(bar) %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates)) %>% 
  mutate(state_id = str_sub(id, 1, 2)) %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  theme_hc() +
  theme(legend.position = "bottom") +
  labs(title = "Sales per Store", x = "Date", y = "Sales", col = "Store ID") +
  facet_wrap(~state_id)

layout <- "
AAB
CCC
"

p1 + p2 + p3 + plot_layout(design = layout)

min_date <- date("2011-01-29")

foo <- train %>%
  group_by(dept_id, state_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  ungroup() %>% 
  select(ends_with("id"), starts_with("d_")) %>%  
  pivot_longer(starts_with("d_"), names_to = "dates", values_to = "sales") %>%
  mutate(dates = as.integer(str_remove(dates, "d_"))) %>% 
  mutate(dates = min_date + dates - 1)

foo %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, dept_id, state_id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates)) %>% 
  ggplot(aes(dates, sales, col = dept_id)) +
  geom_line() +
  facet_grid(state_id ~ dept_id) +
  theme_tufte() +
  theme(legend.position = "none", strip.text.x = element_text(size = 8)) +
  labs(title = "Sales per Department and State", x = "Date", y = "Sales")

foo <- train %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  mutate(id = 1)

bar <- extract_ts(foo) %>% 
  filter(!str_detect(as.character(dates), "-12-25"))

loess_all <- predict(loess(bar$sales ~ as.integer(bar$dates - min(bar$dates)) + 1, span = 1/2, degree = 1))

bar <- bar %>% 
  mutate(loess = loess_all) %>% 
  mutate(sales_rel = sales - loess)

p1 <- bar %>% 
  ggplot(aes(dates, sales)) +
  geom_line(col = "blue", alpha = 0.5) +
  geom_line(aes(dates, loess), col = "black") +
  theme_hc() +
  labs(x = "", y = "Sales", title = "Total Sales with Smoothing Fit + Seasonality in Residuals")

p2 <- bar %>% 
  mutate(wday = wday(dates, label = TRUE, week_start = 1),
         month = month(dates, label = TRUE),
         year = year(dates)) %>% 
  group_by(wday, month, year) %>% 
  summarise(sales = sum(sales_rel)/1e3) %>%
  ggplot(aes(month, wday, fill = sales)) +
  geom_tile() +
  labs(x = "Month of the year", y = "Day of the week", fill = "Relative Sales [1k]") +
  scale_fill_distiller(palette = "Spectral") +
  theme_hc()

p1 / p2

foo <- train %>%
  group_by(store_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = store_id)

bar <- extract_ts(foo) %>% 
  filter(!str_detect(as.character(dates), "-12-25")) %>% 
  group_by(id) %>% 
  mutate(loess = predict(loess(sales ~ as.integer(dates - min(dates)) + 1, span = 1/2, degree = 1)),
         mean_sales = (sales)) %>% 
  mutate(sales_rel = (sales - loess)/mean_sales)

p1 <- bar %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  geom_line(aes(dates, loess), col = "black") +
  facet_wrap(~ id) +
  theme_tufte() +
  theme(legend.position = "none") +
  labs(x = "", y = "Sales", title = "Sales per State with Seasonalities")
idx.CA.1=which(bar$id %in% 'CA_1')
idx.CA.2=which(bar$id %in% 'CA_2')
idx.CA.3=which(bar$id %in% 'CA_3')
idx.CA.4=which(bar$id %in% 'CA_4')

idx.WI.1=which(bar$id %in% 'WI_1')
idx.WI.2=which(bar$id %in% 'WI_2')
idx.WI.3=which(bar$id %in% 'WI_3')

idx.TX.1=which(bar$id %in% 'TX_1')
idx.TX.2=which(bar$id %in% 'TX_2')
idx.TX.3=which(bar$id %in% 'TX_3')

Cal.1<-bar$mean_sales[idx.CA.1]
Cal.2<-bar$mean_sales[idx.CA.2]
Cal.3<-bar$mean_sales[idx.CA.3]
Cal.4<-bar$mean_sales[idx.CA.4]
Cal.1.ts<-ts(Cal.1,start=1,freq=7)
Cal.2.ts<-ts(Cal.2,start=1,freq=7)
Cal.3.ts<-ts(Cal.3,start=1,freq=7)
Cal.4.ts<-ts(Cal.4,start=1,freq=7)
Cal.tot.ts=Cal.1.ts+Cal.2.ts+Cal.3.ts+Cal.4.ts


WI.1<-bar$mean_sales[idx.WI.1]
WI.2<-bar$mean_sales[idx.WI.2]
WI.3<-bar$mean_sales[idx.WI.3]
WI.1.ts<-ts(WI.1,start=1,freq=7)
WI.2.ts<-ts(WI.2,start=1,freq=7)
WI.3.ts<-ts(WI.3,start=1,freq=7)
WI.tot.ts=WI.1.ts+WI.2.ts+WI.3.ts


TX.1<-bar$mean_sales[idx.TX.1]
TX.2<-bar$mean_sales[idx.TX.2]
TX.3<-bar$mean_sales[idx.TX.3]
TX.1.ts<-ts(TX.1,start=1,freq=7)
TX.2.ts<-ts(TX.2,start=1,freq=7)
TX.3.ts<-ts(TX.3,start=1,freq=7)
TX.tot.ts=TX.1.ts+TX.2.ts+TX.3.ts

Wal.tot.ts=Cal.tot.ts+WI.tot.ts+TX.tot.ts

par(mfrow=c(1,3))
plot(Cal.tot.ts,xlab="Time (in weeks)")
plot(WI.tot.ts,xlab="Time (in weeks)")
plot(TX.tot.ts,xlab="Time (in weeks)")


require(dlm)

# Calts<-bar$mean_sales[1:1908]
# WIts<-bar$mean_sales[1909:3816]
# TXts<-bar$mean_sales[3817:5724]
# 
# CA.ts <- ts(Calts,start=1,freq=7)
# WI.ts <- ts(WIts,start=1,freq=7)
# TX.ts <- ts(TXts,start=1,freq=7)

{r} # library(dplyr) # wal <-read.csv(file='sales_train_validation.csv') # dt<-apply(wal, 1, function(r) any(r %in% c("CA"))) # Caldatachk<-as.matrix(wal[dt,7:1919]) # Calts<- colSums(Caldatachk) # dim(Calts) # Cal.ts <- ts(Calts,start=1,freq=7) #

{r} # dt2<-apply(wal, 1, function(r) any(r %in% c("TX"))) # sv<-as.matrix(wal[dt2,7:1919]) # TXdata<- colSums(sv) # TX.ts <- ts(TXdata,start=1,freq=7) # #

```{r}

dt3<-apply(wal, 1, function(r) any(r %in% c(“WI”)))

WIdata<- colSums(as.matrix(wal[dt3,7:1919]))

WI.ts <- ts(WIdata,start=1,freq=7)

plot(WI.ts,xlab=“Time (in days)”)

The three time series for each of the states are represented as above, it clearly shows seasonality, with the christmas day have zero sales. We need to provide such extra bit of information(but how?)

The combined time series shows heavy seasonality as well.



log.CA.ts=log((Wal.tot.ts))
plot(log.CA.ts)


log.WI.ts=sqrt(WI.tot.ts)
plot(log.WI.ts)


log.TX.ts=sqrt(TX.tot.ts)
plot(log.TX.ts)

NA
NA

(AKSHAT), look this chunk of code.

# DLM with polynomial second-order trend and seasonality modeled with a seasonal factor representation.
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))+dlmModTrig(s = 30,q=5, dV = 0, dW=exp(parm[5]))+dlmModTrig(s = 365,q=1, dV = 0, dW=exp(parm[6]))
}
fit <- dlmMLE(log.CA.ts, rep(0,6), build)
fit$convergence
[1] 0
BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(log.CA.ts))
print("BIC")
[1] "BIC"
BIC.2nd.seasfactor
[1] -7277.368
model2 <- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
[1] "Observational noise from MLE"
model2$V
            [,1]
[1,] 0.003208416
print("Innovation variance matrix diagonal elements from MLE")
[1] "Innovation variance matrix diagonal elements from MLE"
model2$W[1:2,1:2]
             [,1]         [,2]
[1,] 6.683947e-05 0.000000e+00
[2,] 0.000000e+00 1.071542e-18
log.CA.filt2 <- dlmFilter(log.CA.ts, model2)

cov.filt <- with(log.CA.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)




seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)






###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.CA.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(log.CA.ts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)


######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
[1] " Mean absolute forecast error"
# Mean absolute forecast error (MAE)
mean(abs(log.CA.filt2$f[1800:1908] - log.CA.ts[1800:1908]))
[1] 0.05948065
print(" Mean squared forecast error (MSE)")
[1] " Mean squared forecast error (MSE)"
# Mean squared forecast error (MSE)
mean((log.CA.filt2$f[1800:1908] - log.CA.ts[1800:1908])^2)
[1] 0.006213475
print(" Mean absolute percentage forecast error (MAPE)")
[1] " Mean absolute percentage forecast error (MAPE)"
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.CA.filt2$f[1800:1908] - log.CA.ts[1800:1908]) / log.CA.ts[1800:1908])
[1] 0.005598321
plot(log.CA.filt2$f,ylim=c(8,12))
lines(log.CA.ts,col="green")

# Following snippet of ccode is for model diagonstics
# Get one-step ahead forecast errors
res <- residuals(log.CA.filt2, sd=FALSE)

# Plot one-step ahead forecast errors

plot(res,type='h'); abline(h=0)
par(mfrow=c(1,2))

acf(res,lag.max = 260)
pacf(res,lag.max = 260)


# Plot qq-plot of one-step ahead forecast errors
qqnorm(res); qqline(res)



# Test normality with the Shapiro-Wilk normality test
# H_0: errors are normally distribution
# H_A: errors are not normally distribution
shapiro.test(res)

    Shapiro-Wilk normality test

data:  res
W = 0.96511, p-value < 2.2e-16
# Test autocorrelation with the Ljung-Box test
# H_0: errors are independent
# H_A: errors exhibit serial correlation
 Box.test(res, lag=20, type="Ljung")   

    Box-Ljung test

data:  res
X-squared = 95.014, df = 20, p-value = 9.723e-12
sapply(1 : 20, function(i)
       Box.test(res, lag = i, type = "Ljung-Box")$p.value)
 [1] 1.233522e-06 9.946891e-10 9.663759e-11 3.415525e-10
 [5] 8.630086e-10 6.781020e-12 7.627676e-12 1.570966e-13
 [9] 2.529088e-13 7.372991e-13 9.876544e-13 2.057465e-12
[13] 5.551892e-12 7.856715e-12 1.892264e-11 4.489142e-11
[17] 8.485157e-11 1.857294e-10 1.818690e-11 9.723111e-12
# DLM with polynomial second-order trend and seasonality modeled with a seasonal factor representation.
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))
}
fit <- dlmMLE(log.WI.ts, rep(0,4), build)
fit$convergence
[1] 0
BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(log.WI.ts))
print("BIC")
[1] "BIC"
BIC.2nd.seasfactor
[1] -6382.772
model.WI <- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
[1] "Observational noise from MLE"
model.WI$V
            [,1]
[1,] 0.007059662
print("Innovation variance matrix diagonal elements from MLE")
[1] "Innovation variance matrix diagonal elements from MLE"
model.WI$W[1:2,1:2]
             [,1]         [,2]
[1,] 0.0001928866 0.000000e+00
[2,] 0.0000000000 1.012899e-13
log.WI.filt2 <- dlmFilter(log.WI.ts, model.WI)

cov.filt <- with(log.WI.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)




seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)






###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.WI.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(log.WI.ts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)


######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
[1] " Mean absolute forecast error"
# Mean absolute forecast error (MAE)
mean(abs(log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908]))
[1] 0.09760941
print(" Mean squared forecast error (MSE)")
[1] " Mean squared forecast error (MSE)"
# Mean squared forecast error (MSE)
mean((log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908])^2)
[1] 0.02638784
print(" Mean absolute percentage forecast error (MAPE)")
[1] " Mean absolute percentage forecast error (MAPE)"
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908]) / log.WI.ts[1800:1908])
[1] 0.01176742
plot(log.WI.filt2$f,ylim=c(9,11))
lines(log.WI.ts,col="green")

NA
NA
# Following snippet of ccode is for model diagonstics
# Get one-step ahead forecast errors
res <- residuals(log.WI.filt2, sd=FALSE)

# Plot one-step ahead forecast errors

plot(res,type='h'); abline(h=0)
par(mfrow=c(1,2))

acf(res,lag.max = 260)
pacf(res,lag.max = 260)


# Plot qq-plot of one-step ahead forecast errors
qqnorm(res); qqline(res)



# Test normality with the Shapiro-Wilk normality test
# H_0: errors are normally distribution
# H_A: errors are not normally distribution
shapiro.test(res)

    Shapiro-Wilk normality test

data:  res
W = 0.92541, p-value < 2.2e-16
# Test autocorrelation with the Ljung-Box test
# H_0: errors are independent
# H_A: errors exhibit serial correlation
 Box.test(res, lag=20, type="Ljung")   

    Box-Ljung test

data:  res
X-squared = 125.17, df = 20, p-value < 2.2e-16
sapply(1 : 20, function(i)
       Box.test(res, lag = i, type = "Ljung-Box")$p.value)
 [1] 9.274980e-09 4.651535e-08 4.268566e-08 1.322641e-10 9.722334e-12 3.068412e-11 4.985268e-11 3.441691e-15 1.010303e-14 6.550316e-15
[11] 1.887379e-15 1.110223e-16 2.220446e-16 2.220446e-16 0.000000e+00 0.000000e+00 0.000000e+00 1.110223e-16 0.000000e+00 0.000000e+00
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))
}
fit <- dlmMLE(log.TX.ts, rep(0,4), build)
fit$convergence
[1] 0
BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(log.TX.ts))
print("BIC")
[1] "BIC"
BIC.2nd.seasfactor
[1] -6774.413
model.TX<- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
[1] "Observational noise from MLE"
model.TX$V
            [,1]
[1,] 0.004209568
print("Innovation variance matrix diagonal elements from MLE")
[1] "Innovation variance matrix diagonal elements from MLE"
model.TX$W[1:2,1:2]
            [,1]         [,2]
[1,] 0.001404132 0.000000e+00
[2,] 0.000000000 4.036832e-14
log.TX.filt2 <- dlmFilter(log.TX.ts, model.TX)

cov.filt <- with(log.TX.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)




seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")

llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)






###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.TX.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(log.TX.ts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)


######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
[1] " Mean absolute forecast error"
# Mean absolute forecast error (MAE)
mean(abs(log.TX.filt2$f[1800:1908] - log.TX.ts[1800:1908]))
[1] 0.06367577
print(" Mean squared forecast error (MSE)")
[1] " Mean squared forecast error (MSE)"
# Mean squared forecast error (MSE)
mean((log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908])^2)
[1] 0.02638784
print(" Mean absolute percentage forecast error (MAPE)")
[1] " Mean absolute percentage forecast error (MAPE)"
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908]) / log.WI.ts[1800:1908])
[1] 0.01176742
plot(log.WI.filt2$f,ylim=c(8,10))
lines(log.WI.ts,col="green")

# Following snippet of ccode is for model diagonstics
# Get one-step ahead forecast errors
res <- residuals(log.TX.filt2, sd=FALSE)

# Plot one-step ahead forecast errors

plot(res,type='h'); abline(h=0)
par(mfrow=c(1,2))

acf(res,lag.max = 260)
pacf(res,lag.max = 260)


# Plot qq-plot of one-step ahead forecast errors
qqnorm(res); qqline(res)



# Test normality with the Shapiro-Wilk normality test
# H_0: errors are normally distribution
# H_A: errors are not normally distribution
shapiro.test(res)

    Shapiro-Wilk normality test

data:  res
W = 0.96155, p-value < 2.2e-16
# Test autocorrelation with the Ljung-Box test
# H_0: errors are independent
# H_A: errors exhibit serial correlation
 Box.test(res, lag=20, type="Ljung")   

    Box-Ljung test

data:  res
X-squared = 176.66, df = 20, p-value < 2.2e-16
sapply(1 : 20, function(i)
       Box.test(res, lag = i, type = "Ljung-Box")$p.value)
 [1] 1.380142e-08 1.718238e-10 1.110223e-16 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
[11] 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00

log.TX.filt2 <- function(newts){
remove(log.TX.ts)
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))
}
fit <- dlmMLE(newts, rep(0,4), build)
fit$convergence

BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(newts))
print("BIC")
BIC.2nd.seasfactor

model.TX<- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
model.TX$V
print("Innovation variance matrix diagonal elements from MLE")
model.TX$W[1:2,1:2]

log.TX.filt2 <- dlmFilter(newts, model.TX)

cov.filt <- with(log.TX.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)

seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)





###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.TX.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(newts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)

######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
# Mean absolute forecast error (MAE)
mean(abs(log.TX.filt2$f[1800:1908] - newts[1800:1908]))

print(" Mean squared forecast error (MSE)")
# Mean squared forecast error (MSE)
mean((log.TX.filt2$f[1800:1908] - newts[1800:1908])^2)

print(" Mean absolute percentage forecast error (MAPE)")
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.TX.filt2$f[1800:1908] - newts[1800:1908]) / newts[1800:1908])

plot(log.TX.filt2$f,ylim=c(8,10))
lines(newts,col="green") 
}
---
title: "R Notebook"
output:
  html_document:
    df_print: paged
  html_notebook: default
  pdf_document: default
---

This is an [R Markdown](http://rmarkdown.rstudio.com) Notebook. When you execute code within the notebook, the results appear beneath the code. 

Try executing this chunk by clicking the *Run* button within the chunk or by placing your cursor inside it and pressing *Ctrl+Shift+Enter*. 

```{r}
# general visualisation
library('ggplot2') # visualisation
library('scales') # visualisation
library('patchwork') # visualisation
library('RColorBrewer') # visualisation
library('corrplot') # visualisation

# general data manipulation
library('dplyr') # data manipulation
library('readr') # input/output
library('vroom') # input/output
library('skimr') # overview
library('tibble') # data wrangling
library('tidyr') # data wrangling
library('purrr') # data wrangling
library('stringr') # string manipulation
library('forcats') # factor manipulation

# specific visualisation
library('alluvial') # visualisation
library('ggrepel') # visualisation
library('ggforce') # visualisation
library('ggridges') # visualisation
library('gganimate') # animations
library('GGally') # visualisation
library('ggthemes') # visualisation
library('wesanderson') # visualisation
library('kableExtra') # display

# Date + forecast
library('lubridate') # date and time
library('forecast') # time series analysis
#library('prophet') # time series analysis
library('timetk') # time series analysis

# Interactivity
library('crosstalk')
library('plotly')

# parallel
library('foreach')
library('doParallel')

```


```{r}
library(vroom)
library(stringr)
library(tidyverse)
train <- vroom(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/sales_train_validation.csv'), delim = ",", col_types = cols())
prices <- vroom(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/sell_prices.csv'), delim = ",", col_types = cols())
calendar <- read_csv(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/calendar.csv'), col_types = cols())

sample_submit <- vroom(str_c('/Coursework/Timeseries/Timeseries_project/CSV files/sample_submission.csv'), delim = ",", col_types = cols())
```

```{r}

extract_ts <- function(df){
  
  min_date <- as.Date("2011-01-29")
  
  df %>%
    select(id, starts_with("d_")) %>%  
    pivot_longer(starts_with("d_"), names_to = "dates", values_to = "sales") %>%
    mutate(dates = as.integer(str_remove(dates, "d_"))) %>% 
    mutate(dates = min_date + dates - 1) %>% 
    mutate(id = str_remove(id, "_validation"))
}

set.seed(4321)
foo <- train %>% 
  sample_n(50)

ts_out <- extract_ts(foo)

cols <- ts_out %>% 
  distinct(id) %>% 
  mutate(cols = rep_len(brewer.pal(7, "Set2"), length.out = n_distinct(ts_out$id)))

ts_out <- ts_out %>% 
  left_join(cols, by = "id")

pal <- cols$cols %>%
   setNames(cols$id)
```

```{r}
shared_ts <- highlight_key(ts_out)

palette(brewer.pal(9, "Set3"))

gg <- shared_ts %>% 
  ggplot(aes(dates, sales, col = id, group = id)) +
  geom_line() +
  scale_color_manual(values = pal) +
  labs(x = "Date", y = "Sales") +
  theme_tufte() +
  NULL

filter <- bscols(
  filter_select("ids", "Sales over time: Select a time series ID (remove with backspace key, navigate with arrow keys):", shared_ts, ~id, multiple = TRUE),
  ggplotly(gg, dynamicTicks = TRUE),
  widths = c(12, 12)
)

bscols(filter)
```
```{r}
foo <- train %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  mutate(id = 1)

bar <- extract_ts(foo)

gg <- bar %>% 
  ggplot(aes(dates, sales)) +
  geom_line(col = "blue") +
  theme_tufte() +
  labs(x = "Date", y = "Sales", title = "All aggregate sales")

ggplotly(gg, dynamicTicks = TRUE)
```
```{r}
foo <- train %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  mutate(id = 1)

bar <- extract_ts(foo)

gg <- bar %>% 
  ggplot(aes(dates, sales)) +
  geom_line(col = "blue") +
  theme_tufte() +
  labs(x = "Date", y = "Sales", title = "All aggregate sales")

ggplotly(gg, dynamicTicks = TRUE)
```
```{r}
foo <- train %>%
  group_by(state_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = state_id)

bar <- extract_ts(foo) %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates))

gg <- bar %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  theme_tufte() +
  labs(x = "Date", y = "Sales", title = "Monthly Sales per State")

ggplotly(gg, dynamicTicks = TRUE)
```





```{r}
foo <- train %>%
  group_by(cat_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = cat_id)

bar <- train %>%
  group_by(store_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = store_id)

p1 <- extract_ts(foo) %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates)) %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  theme_hc() +
  theme(legend.position = "none") +
  labs(title = "Sales per Category", x = "Date", y = "Sales")

p2 <- train %>% 
  count(cat_id) %>% 
  ggplot(aes(cat_id, n, fill = cat_id)) +
  geom_col() +
  theme_hc() +
  theme(legend.position = "none") +
  theme(axis.text.x = element_text(size = 7)) +
  labs(x = "", y = "", title = "Rows per Category")

p3 <- extract_ts(bar) %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates)) %>% 
  mutate(state_id = str_sub(id, 1, 2)) %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  theme_hc() +
  theme(legend.position = "bottom") +
  labs(title = "Sales per Store", x = "Date", y = "Sales", col = "Store ID") +
  facet_wrap(~state_id)

layout <- "
AAB
CCC
"

p1 + p2 + p3 + plot_layout(design = layout)
```

```{r}
min_date <- date("2011-01-29")

foo <- train %>%
  group_by(dept_id, state_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  ungroup() %>% 
  select(ends_with("id"), starts_with("d_")) %>%  
  pivot_longer(starts_with("d_"), names_to = "dates", values_to = "sales") %>%
  mutate(dates = as.integer(str_remove(dates, "d_"))) %>% 
  mutate(dates = min_date + dates - 1)

foo %>% 
  mutate(month = month(dates),
         year = year(dates)) %>% 
  group_by(month, year, dept_id, state_id) %>% 
  summarise(sales = sum(sales),
            dates = min(dates)) %>% 
  ungroup() %>% 
  filter(str_detect(as.character(dates), "..-..-01")) %>% 
  filter(dates != max(dates)) %>% 
  ggplot(aes(dates, sales, col = dept_id)) +
  geom_line() +
  facet_grid(state_id ~ dept_id) +
  theme_tufte() +
  theme(legend.position = "none", strip.text.x = element_text(size = 8)) +
  labs(title = "Sales per Department and State", x = "Date", y = "Sales")
```

```{r}
foo <- train %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  mutate(id = 1)

bar <- extract_ts(foo) %>% 
  filter(!str_detect(as.character(dates), "-12-25"))

loess_all <- predict(loess(bar$sales ~ as.integer(bar$dates - min(bar$dates)) + 1, span = 1/2, degree = 1))

bar <- bar %>% 
  mutate(loess = loess_all) %>% 
  mutate(sales_rel = sales - loess)

p1 <- bar %>% 
  ggplot(aes(dates, sales)) +
  geom_line(col = "blue", alpha = 0.5) +
  geom_line(aes(dates, loess), col = "black") +
  theme_hc() +
  labs(x = "", y = "Sales", title = "Total Sales with Smoothing Fit + Seasonality in Residuals")

p2 <- bar %>% 
  mutate(wday = wday(dates, label = TRUE, week_start = 1),
         month = month(dates, label = TRUE),
         year = year(dates)) %>% 
  group_by(wday, month, year) %>% 
  summarise(sales = sum(sales_rel)/1e3) %>%
  ggplot(aes(month, wday, fill = sales)) +
  geom_tile() +
  labs(x = "Month of the year", y = "Day of the week", fill = "Relative Sales [1k]") +
  scale_fill_distiller(palette = "Spectral") +
  theme_hc()

p1 / p2
```

```{r}
foo <- train %>%
  group_by(store_id) %>% 
  summarise_at(vars(starts_with("d_")), sum) %>% 
  rename(id = store_id)

bar <- extract_ts(foo) %>% 
  filter(!str_detect(as.character(dates), "-12-25")) %>% 
  group_by(id) %>% 
  mutate(loess = predict(loess(sales ~ as.integer(dates - min(dates)) + 1, span = 1/2, degree = 1)),
         mean_sales = (sales)) %>% 
  mutate(sales_rel = (sales - loess)/mean_sales)

p1 <- bar %>% 
  ggplot(aes(dates, sales, col = id)) +
  geom_line() +
  geom_line(aes(dates, loess), col = "black") +
  facet_wrap(~ id) +
  theme_tufte() +
  theme(legend.position = "none") +
  labs(x = "", y = "Sales", title = "Sales per State with Seasonalities")

```

```{r}
idx.CA.1=which(bar$id %in% 'CA_1')
idx.CA.2=which(bar$id %in% 'CA_2')
idx.CA.3=which(bar$id %in% 'CA_3')
idx.CA.4=which(bar$id %in% 'CA_4')

idx.WI.1=which(bar$id %in% 'WI_1')
idx.WI.2=which(bar$id %in% 'WI_2')
idx.WI.3=which(bar$id %in% 'WI_3')

idx.TX.1=which(bar$id %in% 'TX_1')
idx.TX.2=which(bar$id %in% 'TX_2')
idx.TX.3=which(bar$id %in% 'TX_3')

Cal.1<-bar$mean_sales[idx.CA.1]
Cal.2<-bar$mean_sales[idx.CA.2]
Cal.3<-bar$mean_sales[idx.CA.3]
Cal.4<-bar$mean_sales[idx.CA.4]
Cal.1.ts<-ts(Cal.1,start=1,freq=7)
Cal.2.ts<-ts(Cal.2,start=1,freq=7)
Cal.3.ts<-ts(Cal.3,start=1,freq=7)
Cal.4.ts<-ts(Cal.4,start=1,freq=7)
Cal.tot.ts=Cal.1.ts+Cal.2.ts+Cal.3.ts+Cal.4.ts


WI.1<-bar$mean_sales[idx.WI.1]
WI.2<-bar$mean_sales[idx.WI.2]
WI.3<-bar$mean_sales[idx.WI.3]
WI.1.ts<-ts(WI.1,start=1,freq=7)
WI.2.ts<-ts(WI.2,start=1,freq=7)
WI.3.ts<-ts(WI.3,start=1,freq=7)
WI.tot.ts=WI.1.ts+WI.2.ts+WI.3.ts


TX.1<-bar$mean_sales[idx.TX.1]
TX.2<-bar$mean_sales[idx.TX.2]
TX.3<-bar$mean_sales[idx.TX.3]
TX.1.ts<-ts(TX.1,start=1,freq=7)
TX.2.ts<-ts(TX.2,start=1,freq=7)
TX.3.ts<-ts(TX.3,start=1,freq=7)
TX.tot.ts=TX.1.ts+TX.2.ts+TX.3.ts

Wal.tot.ts=Cal.tot.ts+WI.tot.ts+TX.tot.ts

par(mfrow=c(1,3))
plot(Cal.tot.ts,xlab="Time (in weeks)")
plot(WI.tot.ts,xlab="Time (in weeks)")
plot(TX.tot.ts,xlab="Time (in weeks)")

require(dlm)

# Calts<-bar$mean_sales[1:1908]
# WIts<-bar$mean_sales[1909:3816]
# TXts<-bar$mean_sales[3817:5724]
# 
# CA.ts <- ts(Calts,start=1,freq=7)
# WI.ts <- ts(WIts,start=1,freq=7)
# TX.ts <- ts(TXts,start=1,freq=7)
```



# ```{r}
# library(dplyr)
# wal <-read.csv(file='sales_train_validation.csv')
# dt<-apply(wal, 1, function(r) any(r %in% c("CA")))
# Caldatachk<-as.matrix(wal[dt,7:1919])
# Calts<- colSums(Caldatachk)
# dim(Calts)
# Cal.ts <- ts(Calts,start=1,freq=7)
# ```
# 
# 
# ```{r}
# dt2<-apply(wal, 1, function(r) any(r %in% c("TX")))
# sv<-as.matrix(wal[dt2,7:1919])
# TXdata<- colSums(sv)
# TX.ts <- ts(TXdata,start=1,freq=7)
# 
# ```
# 
# 
# ```{r}
# dt3<-apply(wal, 1, function(r) any(r %in% c("WI")))
# WIdata<- colSums(as.matrix(wal[dt3,7:1919]))
# WI.ts <- ts(WIdata,start=1,freq=7)
# plot(WI.ts,xlab="Time (in days)")



The three time series for each of the states are represented as above, it clearly shows seasonality, with the christmas day have zero sales. We need to provide such extra bit of information(but how?)

The combined time series shows heavy seasonality as well. 
```{r}


log.CA.ts=log((Wal.tot.ts))
plot(log.CA.ts)

log.WI.ts=sqrt(WI.tot.ts)
plot(log.WI.ts)

log.TX.ts=sqrt(TX.tot.ts)
plot(log.TX.ts)


```
(AKSHAT), look this chunk of code. 
```{r}
# DLM with polynomial second-order trend and seasonality modeled with a seasonal factor representation.
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))+dlmModTrig(s = 30,q=5, dV = 0, dW=exp(parm[5]))+dlmModTrig(s = 365,q=1, dV = 0, dW=exp(parm[6]))
}
fit <- dlmMLE(log.CA.ts, rep(0,6), build)
fit$convergence

BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(log.CA.ts))
print("BIC")
BIC.2nd.seasfactor

model2 <- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
model2$V
print("Innovation variance matrix diagonal elements from MLE")
model2$W[1:2,1:2]

log.CA.filt2 <- dlmFilter(log.CA.ts, model2)

cov.filt <- with(log.CA.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)

seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.CA.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)





###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.CA.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(log.CA.ts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)

######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
# Mean absolute forecast error (MAE)
mean(abs(log.CA.filt2$f[1800:1908] - log.CA.ts[1800:1908]))

print(" Mean squared forecast error (MSE)")
# Mean squared forecast error (MSE)
mean((log.CA.filt2$f[1800:1908] - log.CA.ts[1800:1908])^2)

print(" Mean absolute percentage forecast error (MAPE)")
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.CA.filt2$f[1800:1908] - log.CA.ts[1800:1908]) / log.CA.ts[1800:1908])

plot(log.CA.filt2$f,ylim=c(8,12))
lines(log.CA.ts,col="green")

```
```{r}
# Following snippet of ccode is for model diagonstics
# Get one-step ahead forecast errors
res <- residuals(log.CA.filt2, sd=FALSE)

# Plot one-step ahead forecast errors

plot(res,type='h'); abline(h=0)
par(mfrow=c(1,2))
acf(res,lag.max = 200)
pacf(res,lag.max = 200)

# Plot qq-plot of one-step ahead forecast errors
qqnorm(res); qqline(res)


# Test normality with the Shapiro-Wilk normality test
# H_0: errors are normally distribution
# H_A: errors are not normally distribution
shapiro.test(res)


# Test autocorrelation with the Ljung-Box test
# H_0: errors are independent
# H_A: errors exhibit serial correlation
 Box.test(res, lag=20, type="Ljung")   
sapply(1 : 20, function(i)
       Box.test(res, lag = i, type = "Ljung-Box")$p.value)
```


```{r}
# DLM with polynomial second-order trend and seasonality modeled with a seasonal factor representation.
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))
}
fit <- dlmMLE(log.WI.ts, rep(0,4), build)
fit$convergence

BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(log.WI.ts))
print("BIC")
BIC.2nd.seasfactor

model.WI <- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
model.WI$V
print("Innovation variance matrix diagonal elements from MLE")
model.WI$W[1:2,1:2]

log.WI.filt2 <- dlmFilter(log.WI.ts, model.WI)

cov.filt <- with(log.WI.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)

seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.WI.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)





###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.WI.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(log.WI.ts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)

######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
# Mean absolute forecast error (MAE)
mean(abs(log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908]))

print(" Mean squared forecast error (MSE)")
# Mean squared forecast error (MSE)
mean((log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908])^2)

print(" Mean absolute percentage forecast error (MAPE)")
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908]) / log.WI.ts[1800:1908])

plot(log.WI.filt2$f,ylim=c(9,11))
lines(log.WI.ts,col="green")


```

```{r}
# Following snippet of ccode is for model diagonstics
# Get one-step ahead forecast errors
res <- residuals(log.WI.filt2, sd=FALSE)

# Plot one-step ahead forecast errors

plot(res,type='h'); abline(h=0)
par(mfrow=c(1,2))
acf(res,lag.max = 260)
pacf(res,lag.max = 260)

# Plot qq-plot of one-step ahead forecast errors
qqnorm(res); qqline(res)


# Test normality with the Shapiro-Wilk normality test
# H_0: errors are normally distribution
# H_A: errors are not normally distribution
shapiro.test(res)


# Test autocorrelation with the Ljung-Box test
# H_0: errors are independent
# H_A: errors exhibit serial correlation
 Box.test(res, lag=20, type="Ljung")   
sapply(1 : 20, function(i)
       Box.test(res, lag = i, type = "Ljung-Box")$p.value)

```


```{r}
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))
}
fit <- dlmMLE(log.TX.ts, rep(0,4), build)
fit$convergence

BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(log.TX.ts))
print("BIC")
BIC.2nd.seasfactor

model.TX<- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
model.TX$V
print("Innovation variance matrix diagonal elements from MLE")
model.TX$W[1:2,1:2]

log.TX.filt2 <- dlmFilter(log.TX.ts, model.TX)

cov.filt <- with(log.TX.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)

seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)





###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.TX.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(log.TX.ts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)

######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
# Mean absolute forecast error (MAE)
mean(abs(log.TX.filt2$f[1800:1908] - log.TX.ts[1800:1908]))

print(" Mean squared forecast error (MSE)")
# Mean squared forecast error (MSE)
mean((log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908])^2)

print(" Mean absolute percentage forecast error (MAPE)")
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.WI.filt2$f[1800:1908] - log.WI.ts[1800:1908]) / log.WI.ts[1800:1908])

plot(log.WI.filt2$f,ylim=c(8,10))
lines(log.WI.ts,col="green")

```

```{r}
# Following snippet of ccode is for model diagonstics
# Get one-step ahead forecast errors
res <- residuals(log.TX.filt2, sd=FALSE)

# Plot one-step ahead forecast errors

plot(res,type='h'); abline(h=0)
par(mfrow=c(1,2))
acf(res,lag.max = 260)
pacf(res,lag.max = 260)

# Plot qq-plot of one-step ahead forecast errors
qqnorm(res); qqline(res)


# Test normality with the Shapiro-Wilk normality test
# H_0: errors are normally distribution
# H_A: errors are not normally distribution
shapiro.test(res)


# Test autocorrelation with the Ljung-Box test
# H_0: errors are independent
# H_A: errors exhibit serial correlation
 Box.test(res, lag=20, type="Ljung")   
sapply(1 : 20, function(i)
       Box.test(res, lag = i, type = "Ljung-Box")$p.value)

```
```{r}

extract_func_ts <- function(newts){
remove(log.TX.ts)
build <- function(parm) {
  dlmModPoly(order = 2, dV = exp(parm[1]), dW = c(exp(parm[2]),exp(parm[3]))) + dlmModTrig(s = 7, dV = 0, dW=exp(parm[4]))
}
fit <- dlmMLE(newts, rep(0,4), build)
fit$convergence

BIC.2nd.seasfactor <-  2 *  fit$value + length(fit$par) * log(length(newts))
print("BIC")
BIC.2nd.seasfactor

model.TX<- build(fit$par)  #This is part where he takes the model parameters
print("Observational noise from MLE")
model.TX$V
print("Innovation variance matrix diagonal elements from MLE")
model.TX$W[1:2,1:2]

log.TX.filt2 <- dlmFilter(newts, model.TX)

cov.filt <- with(log.TX.filt2, dlmSvd2var(U.C, D.C))

seas.term = 2

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)

seas.term = 4

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)



seas.term = 6

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)


seas.term = 8

sd.seasonality.filt2 <- rep(NA,length(cov.filt))
for(i in 1:length(cov.filt)) sd.seasonality.filt2[i] = sqrt(cov.filt[[i]][seas.term,seas.term])
sd.seasonality.filt2 = ts(sd.seasonality.filt2[-(1:8)],frequency=7)
seasonality.filt2 = ts(log.TX.filt2$m[-(1:8),seas.term],frequency=7)
ll = seasonality.filt2 - 1.96 * sd.seasonality.filt2
ul = seasonality.filt2 + 1.96 * sd.seasonality.filt2
llim = min(ll)
ulim = max(ul)
plot(seasonality.filt2,ylim=c(llim,ulim))
lines(ll,lty=2,col="green")
lines(ul,lty=2,col="green")
llim = min(c(min(seasonality.filt2/sd.seasonality.filt2),-1.96))
ulim = max(c(max(seasonality.filt2/sd.seasonality.filt2),1.96))
plot(seasonality.filt2/sd.seasonality.filt2,ylim=c(llim,ulim))
abline(h=1.96,lty=2)
abline(h=-1.96,lty=2)





###################
#   Forecasting   #
###################

predictions <- dlmForecast(log.TX.filt2, n=28)

ll = predictions$f - 1.96 * sqrt(unlist(predictions$Q))
ul = predictions$f + 1.96 * sqrt(unlist(predictions$Q))
plot(newts, xlab = "", col = "darkgrey",xlim=c(250,300),lwd=2)
#plot(log.choc, xlab = "", col = "darkgrey",xlim=c(1958,2000), ylim=c(1000,10000),lwd=2)
lines(predictions$f, col="red",lwd=2)
lines(ll,lty=2, col="green",lwd=2)
lines(ul,lty=2, col="green",lwd=2)

######################################################
#          One-step ahead forecast error for the last 9 years                #
######################################################
print(" Mean absolute forecast error")
# Mean absolute forecast error (MAE)
mean(abs(log.TX.filt2$f[1800:1908] - newts[1800:1908]))

print(" Mean squared forecast error (MSE)")
# Mean squared forecast error (MSE)
mean((log.TX.filt2$f[1800:1908] - newts[1800:1908])^2)

print(" Mean absolute percentage forecast error (MAPE)")
# Mean absolute percentage forecast error (MAPE)
mean(abs(log.TX.filt2$f[1800:1908] - newts[1800:1908]) / newts[1800:1908])

plot(log.TX.filt2$f,ylim=c(8,10))
lines(newts,col="green") 
}
```

